CBSE Class 10 Mathematics Areas related to circles MCQs

Question : Area of the largest triangle inscribed in a semi-circle of radius r units is
(a.) r² sq. units
(b.) (1/2) r² sq. units
(c.) 2r² sq. units
(d.) √2 r² sq. units
Answer : A

Question : Radii of two circles are 4 cm and 3 cm respectively. There is another circle, which is having area equal to the sum of the areas of two circles whose radii are known. Find the diameter (in cm) of the third circle.
(a.) 5
(b.) 7
(c.) 0
(d.) 14
Answer : C

Question : If 1/2x - 1/y = – 1 and 1/x + 1/2y = 8, (x ≠ 0, y ≠ 0), then
(a) x = 1/4 , y = 1/2
(b) x = 1/3, y = 1/5
(c) x = 1/6, y = 1/8
(d) x = 1/6, y = 1/4
Answer : D

Question : If θ is the angle in degrees of a sector of a circle of radius r units, then the area of the sector is
(a.) Πr²θ/360
(b.) πr²θ/180
(c.) 2πrθ/360
(d.) 2πrθ/180
Answer : A

Question : Which ratio is denoted by a constant known as π
(a.) 𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟/𝐶𝑖𝑟𝑐𝑢𝑚𝑓𝑒𝑟𝑒𝑛𝑐𝑒
(b.) 𝐴𝑟𝑒𝑎/𝐶𝑖𝑟𝑐𝑢𝑚𝑓𝑒𝑟𝑒𝑛𝑐𝑒
(c.) 𝐶𝑖𝑟𝑐𝑢𝑚𝑓𝑒𝑟𝑒𝑛𝑐𝑒/𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟
(d.) 𝐴𝑟𝑒𝑎/𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟
Answer : C

Question : If the circumference of a circle and the perimeter of a square are equal, then the
(a.) Area of the circle = Area of the square
(b.) Area of the circle > Area of the square
(c.) Area of the circle < Area of the square
(d.) We cannot definitely say about the relation between area of the circle and the square
Answer : B

Question : Find area of the largest circle that can be drawn inside a rectangle with length a cm and breadth b cm. (a > b).
(a.) 𝑎²𝜋/4 cm²
(b.) 𝑏²𝜋/2 cm²
(c.) 𝑏²𝜋/4 cm²
(d.) 𝑎²𝜋/2 cm²
Answer : B

Question : The ratio of areas of two circles whose ratio of circumferences is in the ratio of 3 : 1 will be
(a.) 3 : 1
(b.) 1 : 3
(c.) 1 : 9
(d.) 9 : 1
Answer : D

Question : Area of a square is same as area of a circle. What will be the ratio of their perimeters?
(a.) 1 : 1
(b.) π : √2
(c.) 2 : √𝜋
(d.) None of these
Answer : C

Question : The minute hand of a clock is 14 cm long . The area described by it on the face of the clock in 5 minutes is
(a.) 51.33 cm²
(b.) 15.33 cm²
(c.) 21.15 cm²
(d.) 12.35 cm²
Answer : A

Question : A display board is in the shape of a circle. While designing the board, if diameter of the board is increased by 40% from the previous design, then the area will be increased by
(a.) 40%
(b.) 80%
(c.) 96%
(d.) 45%
Answer : C

Question. The area of a circular ring formed by two concentric circles whose radii are 5.7 cm and 4.3 cm respectively is (Take 𝜋=3.14)
(a) 44 sq. cm.
(b) 66 sq. cm.
(c) 22 sq. cm.
(d) 33 sq. cm
Answer : A

Question.The area of a circle is 154 cm, then its diameter is
(a) 7𝑐𝑚
(b) 21𝑐𝑚
(c) 40𝑐𝑚
(d) 28𝑐𝑚
Answer : C

Question. The diameter of a wheel is 40 cm. How many revolutions will it make on covering 176 m ?
(a) 140
(b) 150
(c) 160
(d) 166
Answer : A

Question. The perimeter of circular field is 242 cm. The area of the field is :-
(a) 9317 cm²
(b)18634 cm²
(c) 4658.5 cm²
(d) None of these
Answer : C

Question. The diameter of a wheel is 1.26 metres. How long will it travel in 500 revolutions?
(a) 1492
(b) 2530
(c) 1980
(d) 2880
Answer : C

Question. The difference between the circumference and radius of a circle is 37 cm. The area of the circle is:-
(a) 111cm²
(b) 184 cm²
(c) 154 cm²
(d) 259 cm²
Answer : C

CASE STUDY QUESTION 

Q1. Pookalam is the flower bed or flower pattern designed during Onam in Kerala. It is similar as Rangoli in North India and Kolam in Tamil Nadu. During the festival of Onam, your school is planning to conduct a Pookalam competition. Your friend who is a partner in competition, suggests two designs given below.

Observe these carefully.

Design I: This design is made with a circle of radius 32cm leaving equilateral triangle ABC in the middle as shown in the given figure.
Design II: This Pookalam is made with 9 circular design each of radius 7cm.

Refer Design I:

Question : Find the side of equilateral triangle is
Answer : 32√3 cm

Question : Find the altitude of the equilateral triangle is
Answer : 48cm

Refer Design II:

Question : Find the area of square is
Answer : 1764 m²

Q2. In figure, O is the centre of a circle such that diameter AB = 13 cm and AC = 12 cm. BC is joined. Find the area of the shaded region.

Question : Find the perimeter of circle.
Answer : 40.85 cm

Question : Find the area of triangle.
Answer : 30 cm²

Question : Find the area of shaded portion.
Answer : 36.33 cm²

Question : The area of a circle is 49 πcm². Its circumference is
(a) 7π cm
(b) 14π cm
(c) 21π cm
(d) 28π cm

Question : The perimeter of circular field is 242cm. The area of the field is
(a) 9317 cm²
(b) 18634 cm²
(c) 4658.5 cm²
(d) none of these

Question : The area of a circle is 38.5 cm². Its circumference is
(a) 62 cm
(b) 12.1 cm
(c) 11 cm
(d) 22 cm

Question : The difference between the circumference and radius of a circle is 37 cm. The area of the circle is
(a) 111 cm²
(b) 184 cm²
(c) 154 cm²
(d) 259 cm²

Question : The circumference of two circles are in the ratio 2 : 3. The ratio of their areas is
(a) 2 : 3
(b) 4 : 9
(c) 9 : 4
(d) none of these

Question : On increasing the diameter of circle by 40%, its area will be increased by
(a) 40%
(b) 80%
(c) 96%
(d) none of these

Question : On decreasing the radius of the circle by 30%, its area is decreased by
(a) 30%
(b) 60%
(c) 45%
(d) none of these

Question : The area of the square is the same as the area of the circle. Their perimeter re in the ratio
(a) 1 : 1
(b) π : 2
(c) 2 : π 
(d) none of these

Question : The areas of the two circle are in the ratio 4 : 9. The ratio of their circumference is
(a) 2 : 3
(b) 4 : 9
(c) 9 : 4
(d) 4 : 9

Question : In making 1000 revolutions, a wheel covers 88 km. The diameter of the wheel is
(a) 14 m
(b) 24 m
(c) 28 m
(d) 40 m

Question : The diameter of a wheel is 40 cm. How many revolutions will it make an covering 176 m?
(a) 140
(b) 150
(c) 160
(d) 166

Question : The radius of wheel is 0.25 m. How many revolutions will it make in covering 11 km?
(a) 2800
(b) 4000
(c) 5500
(d) 7000

Question : Find the circumference of a circle of diameter 21 cm.
(a) 62 cm
(b) 64 cm
(c) 66 cm
(d) 68 cm

Question : Find the area of a circle whose circumference is 52.8 cm.
(a) 221.76 cm²
(b) 220.76 cm²
(c) 200.76 cm²
(d) none of these.

Question : A steel wire when bent in the form of a square, encloses an area of 121 sq. cm. The same wire is bent in the form of a circle. Find the area of the circle.
(a) 111 cm²
(b) 184 cm²
(c) 154 cm²
(d) 259 cm²